Rigourous Methods - Unit Operations - Lecture Slides, Slides of Engineering Chemistry

Multicomponent Distillation, Mass transport theories , Principles of adsorption , Principles of humidification , Principles of drying are main topics covered in this Unit Operations course. This lecture covers following points: Rigourous Methods, Distillation Process, Thermodynamic System, Equilibrium Stage, Material Balance Equations, Equilibrium Relations, Degrees of Freedom Analysis, Design Strategy, Stage Efficiency Analysis, Thermodynamics Data

Typology: Slides

2012/2013

Uploaded on 08/30/2013

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Rigorous methods for multicomponent
distillation process
General representation of an equilibrium stage
as a thermodynamic system:
Stage j
F
j
F
j
F
jjij TPhzF ,,,, ,j
Q
11
11,1
,
,,,
jj
L
jjij
TP
hxL
11
11,1
,
,,,
jj
V
jjij
TP
hyV
jj
L
jjij
TP
hxL
,
,,, ,
jj
V
jjij
TP
hyV
,
,,, ,
j
U
j
W
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pf9
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Rigorous methods for multicomponentdistillation processGeneral representation of an equilibrium stageas a thermodynamic system:

Stage j

F j F j

F j ji j^

T P h z F

,

, , ,^

,^

j Q

1 1

1 1 , 1 ,

, ,

,

 

 

j j

L j ji

j

T P

h

x

L

1 1

1 1 , 1 ,

, ,

,

 

 

j j

V j ji

j

T P

h

y

V

j j

L j ji j

T P

h x L

,

, , ,^

,

j j

V j ji j

T P

h y V

,

, , ,^

,

j U

j W

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Rigorous methods for multicomponentdistillation process

1. M: Material balance equations:

0

)

(

)

(^

       

^

j i j j j i j j j i j j i j

ji

j

ij^

y W V x U L z F y V x L M

  • There should be C equations for each stage

2. E: Equilibrium relations:

0

,^

j

i

ij

ji

ij^

x K

y

E

  • There should be C equations for each stage

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Rigorous methods for multicomponentdistillation process

Degrees of freedom analysis:

Total number of equations:

N (2C+3)

Unknowns:

ji

ji

ji

y

x z^

,^

,

,^

j j j

j j F j F j j j j^

Q W U T P T P F L V , , , , , , , , ,

3C

N(3C+10)+

N itself

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Rigorous methods for multicomponentdistillation process

Thermodynamics relations:

j

i j

j

V j

j i j

j

L j

j i j i j j

ij

y

P

T

f

h

x

P

T

f

h

y x P T f K

,^ ,

,

,

(Once we know temperature, pressureand composition of a stream we cancalculate thermodynamic properties of thestream using P-v-T equation of states andactivity coefficients models)

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Rigorous methods for multicomponentdistillation process

General solution strategy: The idea is to rewrite the first 3 of MESH equations so to eliminatey and L:

j j i j j i j j i

j^

D x C x B x A 

 ^

,

,

1 ,

where

N j

z F

D

N j

K V

C

N j K W V U V U W F V B

N j V U W F V A

ji
j
j
ji
j
j
ij
j j j m m m
j m
j
j
j m
m
m
m
j
j

 

 

 

          

      

 

1

1

1

1 ] ) ( ) ( [

2

)

(

Note that these equations nowcontain only V and x as unknowns

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Rigorous methods for multicomponentdistillation process

General solution strategy: In matrix form:

N

i i i Ni N N^

D D D D

x x x x B A

C B A

C
B
B A
A

1 2 3

(^1) , (^2) , (^3) , ,

3 3 3

2 2 1 2 1

Given

V

and

T

values for each stage we can solvethis matrix for each component to obtainmole fraction of component

i^

in liquid phase

at each stage

j^

( x

) i,j   

C i

j j i i

correctedji

j i

j j

x x

x

x

T V

1

, ,

,

,

) , (

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Rigorous methods for multicomponentdistillation process

General solution strategy: In a similar way we can compose another set of equations using the enthalpybalance:

^                     

 ^

N

N

N N

V
V V V V

3 4

(^22) 2

3 4 5 1 1

4 2 4 2 3

Given

T,

( x

), ( i,j

y^ i,j

values for each stage we can solvethis matrix for each stage to calculatevapour flow rate for the stage

V

j j j i j i

j^

V

y

x T

 )

,

, (^

,

,

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Rigorous methods for multicomponentdistillation process

Complete design strategy:

,^

, , , , , , , , ,

,^

L V Q W U P T P F z N

j

j

j

j

F j

F j

j

j

i

Specify

1. Guess

) , (^

j j^

T V

  

C i

ji ji

correctedji

ji

j j

x x

x

x

T V

) , (

2. Solvematrix

3. Compute

T

from j

the bubble pointcalculation.Calculate

y

ij

j

ji ji j^

V

y x T^

)

, , (^

4. Solve thesecond matrix

5. New

L

j

6. Check convergenceIf no -> repeat the cycle

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